What are the Factors of 2717?

The following are the different types of factors of 2717:

• Factors of 2717: 1, 11, 13, 19, 143, 209, 247, 2717

• Sum of Factors of 2717: 3360

• Negative Factors of 2717: -1, -11, -13, -19, -143, -209, -247, -2717

• Prime Factors of 2717: 11, 13, 19

• Prime Factorization of 2717: 11^1 × 13^1 × 19^1

There are two ways to find the factors of 2717: using factor pairs, and using prime factorization.

Factor pairs of 2717 are any two numbers that, when multiplied together, equal 2717. The question to ask is “what two numbers multiplied together equal 2717?” Every factor can be paired with another factor, and multiplying the two will result in 2717.

To find the factor pairs of 2717, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2717. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 11.

Step 2:

Divide 2717 by the smallest prime factor, in this case, 11:

2717 ÷ 11 = 247

11 and 247 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 247 as the new focus. Find the smallest prime factor that isn’t 1, and divide 247 by that number. In this case, 13 is the new smallest prime factor:

247 ÷ 13 = 19

Remember that this new factor pair is only for the factors of 247, not 2717. So, to finish the factor pair for 2717, you’d multiply 11 and 13 before pairing with 19:

11 x 13 = 143

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 2717:

(1, 2717), (11, 247), (13, 209), (19, 143)

So, to list all the factors of 2717: 1, 11, 13, 19, 143, 209, 247, 2717

The negative factors of 2717 would be: -1, -11, -13, -19, -143, -209, -247, -2717

To find the Prime factorization of 2717, we break down all the factors of 2717 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.

The process of finding the prime factorization of 2717 only has a few differences from the above method of finding the factors of 2717. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 2717:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 2717. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 11.

Step 2:

Divide 2717 by the smallest prime factor, in this case, 11

2717 ÷ 11 = 247

11 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 247 as the new focus. Find the smallest prime factor that isn’t 1, and divide 247 by that number. The smallest prime factor you pick for 247 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 2717 are: 11, 13, 19

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 105 - The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

Factors of 79 - The factors of 79 are 1, 79

Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128

Factors of 86 - The factors of 86 are 1, 2, 43, 86